The Cult of Pythagoras

Math and Myths

Alberto A. Martinez

Publication Year: 2012

Martínez discusses various popular myths from the history of mathematics. Some stories are partly true, others are entirely false, but all show the power of invention in history. Martínez inspects a wealth of primary sources, in several languages, over a span of many centuries. By exploring disagreements and ambiguities in the history of the elements of mathematics, The Cult of Pythagoras dispels myths that obscure the actual origins of mathematical concepts.

Introduction

The international bestseller The Secret claims that Pythagoras knew the secret
to happiness, the powerful law of attraction: that you can get what you
want by thinking about it. Less recently, in one of the most popular science
books ever, Carl Sagan noted that on the island of Samos local tradition says
that their native son Pythagoras ...

1. Triangle Sacrifi ce to the Gods

Legends say that in ancient times a secretive cult of vegetarians was led by
a man who had a strange birthmark on his thigh and who taught that we
should not eat beans. He believed that when a person dies, the soul can be
reborn in another body, even as an animal. So he said that we should not
eat animals because they might be our dead relatives or friends. ...

2. An Irrational Murder at Sea

If not Pythagoras himself, at least some of his admirers seemed to be
interested in mathematics. Yet the earliest evidence is not complimentary. It
suggests that some Pythagoreans focused on numbers not too thoughtfully.
Plato criticized the Pythagoreans for analyzing numerically the harmonies of
plucked strings, rather than analyzing relations among numbers themselves.1 ...

3. Ugly Old Socrates on Eternal Truth

There is no good evidence that Pythagoras linked mathematics and
religion, but apparently someone else did. Socrates lived in Athens in
the fifth century BCE. According to ancient accounts, he was very ugly, with
bulging eyes and a flat, upturned nose with wide-open nostrils. Allegedly he
became a soldier and fought bravely in some battles. ...

4. The Death of Archimedes

The idea that geometry is timeless led people to think that there can be
no change in mathematics. There can be discovery, they thought, but
not invention. It also encouraged the idea that change and moving things
are foreign to pure mathematics. Euclid seemed to have purifi ed geometry,
although Archimedes later mixed it with practical things. ...

5. Gauss, Galois, and the Golden Ratio

We tend to fit history into the forms of traditional stories about heroes,
victims, and martyrs, struggle, success, and injustice. Hence we read:
“From of old it has been the custom, and not in our time only, for vice to
make war on virtue. Thus Pythagoras, with three hundred others, was burnt
to death.”1 But really, we do not know just how Pythagoras died. ...

6. From Nothing to Infinity

Mathematicians have the distinction of agreeing about results more often
than members of most other professions. I think that mathematicians
usually agree with one another more than the members of any science,
any political party, and even any religion. But nevertheless, we can consider
instances in which mathematicians have disagreed about various things, ...

7. Euler’s Imaginary Mistakes

These steps seem to prove the impossible equation, that 1 is equal to its opposite.
We expect that something in the sequence of operations must be a
mistake. What is it? I will give an original solution to this apparent paradox,
and to do so, I’ll fi rst explain the forgotten arguments of a famous mathematician,
Leonhard Euler. ...

8. The Four of Pythagoras

Some teachers love this: it seems to clearly give meaning to complex
numbers by connecting numbers and geometry: every single number, real
or complex, corresponds uniquely to a single point in a plane. If we take this
sheet of paper, this page, as representing the complex plane, then the period
at the end of this sentence corresponds to a single complex number. ...

9. The War over the Infinitely Small

Scientists used to say that matter is made of indivisible units, atoms. But
some thought that matter is divisible into fragments much smaller. In
1896, physicist Emil Wiechert commented: “We might have to forever abandon
the idea that by going toward the Small we shall eventually reach the
ultimate foundations of the universe, ...

10. Impossible Triangles

When Albert Einstein was a solitary boy, less than twelve years old, his
uncle told him about the Pythagorean theorem. The boy struggled to
confi rm it until he devised a way to prove it to himself.1 By reflex, one might
be tempted to construe this anecdote as early evidence that Einstein was a
genius, but no—he didn’t see it that way, ...

11. Inventing Mathematics?

Through the so-called Platonist outlook, many people construed mathematics
in religious ways. They assumed that its principles were eternal
truths discovered by special men, geniuses, and they accepted that these
truths were valid everywhere and could never change. The laws of geometry
and numbers seemed like the laws of God, ...

12. The Cult of Pythagoras

Mythology deals with gods and heroes, tales that are passed down especially
in popular oral traditions. We began with Pythagoras, in a time
when religion and science mixed. I don’t know if he really contributed anything
to mathematics, but he became portrayed in the form of classic myths:
a wise demigod who started a Golden Age,
...

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